Since the work of Rippl in 1883, researchers have experimented and suggested many approaches in determining the appropriate capacity of a dam. In 1954, P.A.P. Moran introduced the probability theory of dams. This is now an active branch of Applied Probability. Since the introduction of probability theory of dams, probabilistic considerations have been practiced in determining the capacity of a dam. Various researchers determined the capacity by using stationary distribution of the dam content, by considering Mean of the First Emptiness time, and by specifying the probability of overflow of a dam. But the two important events-probability of emptiness and the time at which the dam overflows for the first time were not considered simultaneously in determining the capacity.

In this study, we briefly defined the dam model and the importance of capacity determination. We have reviewed the existing methods of determination of the capacity of dams. These methods are of various types-some are directly statistical techniques and some practiced by the design engineers. In our study, the methods used by the design engineers and use of probabilistic consideration at various stages of the process of determining the capacity are highlighted. For determining the capacity of a dam at a certain place, studying the behavior of inflow pattern is essential. Unfortunately, in most cases either the flow records are not available or available for a shorter period of time. Thus augmentation of the input series by generating longer series using simulation technique is essential. In our study, we have used the 34 years historical inflow record of Mitta Mitta river of Australia. As we have studied to determine the capacity by some new technique and not to study the characteristics of any particular stream, any long record would have served our purpose. Mitta Mitta rive of Australia have chosen because of it's long historical record. Analyzing the record, we have found that first order autoregressive log-normal distribution was the best fit for the annual inflow records and Gamma-type distribution fitted well for the monthly inflow records. So, Troutman's (1978) log-normal autoregressive model for annual inflows and Thomas and Fiering's (1962) seasonal model have been used for monthly inflow generatio.

After generating long input series by simulation, we have determined the capacity by considering probability of emptiness of the dam and average first overflow period together. Capacity has been determined for both annual and monthly inflows. For capacity determination using annual inflows we have assumed inflow and release as annual events while for capacity determination using monthly inflows, we have considered monthly input and monthly release. A capacity determined by this approach have found to have chance of emptiness at a given level, and the estimated capacity ensured that the time at which the dam overflows for the first time during a given period is the largest among other time periods at which first overflow occurs. A general Storage-Reliability relationship is also obtained by which annual capacity can be obtained for different values of annual mean inflow and inflow standard deviation.